I took a look at this, and I guess there is a short answer and then a long answer.
Short answer is I think it is very likely the Q45 sensor works in the QX4, and are the same part.
>> Infiniti says the vehicles share the same adaptive cruise system. (But don't specifically say this part is interchangeable anywhere.)
>> The wiring pinouts on the sensor plugs are the same.
>> The operating voltages on the CANBUS sensor circuit are the same.
>> The adjustment procedure and laser aimpoints are the same for both vehicles.
If you decide to try the Q45 sensor, the Q45 mounting bracket needs to be swapped for the QX4 mounting bracket. Those brackets are adjustable, so you must be careful not to change any adjustment settings so the new sensor is aimed exactly the same as the old sensor.
The Q45 sensors ending in AR220 are the newest versions, so try to get one of those versus the earlier parts.
There is still a chance a Q45 sensor won't work. There is nothing that directly says these parts are interchangeable. However, the operating parameters are the same, and wiring is the same, and the sensors look the same. When looking at the parts diagrams for the Q45 and QX4 I noticed that the sensors have different bumper mount points. The sensor mounting brackets are not available separately, so I think the only real difference may be that a QX4 sensor or a Q45 sensor are sold with different mounting brackets, hence the different part numbers.
You should be able to plug in a new sensor, set it flat with face forward, then clear your cruise control codes and reperform the cruise control check you did earlier. You should get no codes. At that point, you can switch brackets and finish the install if all is well.
If there are no codes, but it is not performing well in traffic, you would need to have the dealer do the aiming adjustment. No way to do that yourself.
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Now the longer answer since this took some research. Might as well document it in case someone finds it useful in the future. For a lot of people this is the TLDR part!
>> The 2002 Q45 is a CANBUS vehicle, which replaced OBDII. QX4's are OBDII. In CANBUS all the vehicle computers are connected to a common data link, much like a regular PC. Different systems, so the Q45 and QX4 Intelligent Cruise Controller (Computer) are not the same. The 2002 QX4 ICC however, has a CANBUS sensor operating circuit designed into it which appears to mimic the Q45 CANBUS. (CANBUS circuits are designated by alternating black and white dashes in Infiniti / Nissan cicuit diagrams.)
The sensor circuit works on pins 3 and 6, and has the same operating voltages as the Q45. This is what allows the same sensor to be used on both vehicles. See page EL-306 for the QX4 and page ACS-56 for the Q45 where the sensor circuit parameters are listed. Pinouts are also listed here, and are the same (pins 1,3,4,6).
>> Resistance test for the sensor circuit are the same on both vehicles: 54 to 66 ohms. See page EL-321 for the QX4 and page LAN-64 for the Q45. There is a resistor in the QX4 wiring diagram for this cicuit which is there to mimic the resistance in the Q45 CANBUS circuit I believe.
>> I located an Infiniti dealer tech bulletin that discusses how the technician is supposed to set up the laser adjustment tools for the sensor. This bulletin indicates that the Q45 and QX4 are adjusted to the same specs. Link is here:
http://www.infinitig37.com/TSB/1RB14.pdf
>>Turns out that the staement that the adaptive cruise system is shared with the Q45 came from the 2002 QX4 press release about the vehicle. That statement is a marketing statement, and is only partially true. The underhood components are in many cases the same, but the cruise control computer is different as it is CANBUS. The laser sensor appears to be the same other than the brackets as discussed above.
>> It looks like early QX56's may use this same sensor, but I did not try to verify that.
End of TLDR!